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Let f: R → R be defined as f(x) = x4. Choose the correct answer.
(A) f is one-one onto (B) f is many-one onto
(C) f is one-one but not onto (D) f is neither one-one nor onto
Asked by Mary Last Modified
Answer f: R → R is defined as
Let x, y ∈ R such that f(x) = f(y).
∴
does not imply that
.
For instance,
∴ f is not one-one.
Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2.
∴ f is not onto.
Hence, function f is neither one-one nor onto.
The correct answer is D.
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Sherine Das
Well Qualified and Certified Mathematics B.Ed(M.G Usty)Teacher with more than13 years of Experience
f :R →R is defined as Let x, y ∈ R such that f(x) = f(y). ∴does not imply that. For example f(1)=f(-1)=1∴ f is not one-one. Consider an element 2 ∈ R. It is clear that there does not exist any x in domain R such that f(x) = 2. ∴ f is not onto. Therefore the answer is: D.
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